For transmission of a data packet in a local area network (LAN), the data packet may be packed into a frame. A MAC address (MAC=Media Access Control) of a target computer may be entered into said frame. On the basis of the MAC address valid in the local network the data packet may be sent to the target computer. Using a protocol as ARP (Address Resolution Protocol), the MAC address valid in the local network corresponding to an IP address of the target computer may be requested by a network element which forwards the data packet. Assignments of the MAC address to an IP address of the target computer, or vice versa, may be stored in an address table. Then, assignments do not have to be determined for each data packet to be sent to a specific target computer of the LAN. The address assignments in this address table may be provided with a timer value limiting a period of validity of the address assignment. After time-out an address assignment may be deleted from the address table.